Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces

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2016

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Cambridge : arXiv

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http://arxiv.org/abs/1601.02819

Abstract

We prove interior H2s−ε regularity for weak solutions of linear elliptic integro-differential equations close to the fractional s-Laplacian. The result is obtained via intermediate estimates in Nikol'skii spaces, which are in turn carried out by means of an appropriate modification of the classical translation method by Nirenberg.

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Integro-differential equations, fractional Laplacian, regularity theory, Nirenberg’s translation method, Caccioppoli inequality, fractional Sobolev spaces, Nikol’skii spaces

Keywords GND

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Report

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publishedVersion

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https://oa.tib.eu/renate/handle/123456789/3488

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Mathematik

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